Spanning configurations and matroidal representation stability

Brendan Pawlowski, Eric Ramos, Brendon Rhoades

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Let V1,V2,… be a sequence of vector spaces where Vn carries an action of Ϭn for each n. Representation stability describes when the sequence Vn has a limit. An important source of stability arises when Vn is the dth homology group (for fixed d) of the configuration space of n distinct points in some topological space X. We replace these configuration spaces with the variety Xn,k of spanning configurations of n-tuples (ℓ1,…, ℓn) of lines in ℂk with ℓ1 +… + ℓn = ℂk as vector spaces. That is, we replace the configuration space condition of distinctness with the matroidal condition of spanning. We study stability phenomena for the homology groups Hd(Xn,k) as the parameter (n, k) grows. We also study stability phenomena for a family of multigraded modules related to the Delta Conjecture.

Original languageEnglish
Article number57
JournalSeminaire Lotharingien de Combinatoire
Issue number84
StatePublished - 2020

Keywords

  • representation stability
  • subspace configuration
  • symmetric group module

Fingerprint

Dive into the research topics of 'Spanning configurations and matroidal representation stability'. Together they form a unique fingerprint.

Cite this